Abstract. As a generalization of the concept of a fuzzy implicative fil-ter which is introduced by Liu and Li [3], the notion of (∈,∈∨q k )-fuzzyimplicative filters is introduced, and related properties are investigated.The relationship between (∈, ∈∨q k )-fuzzy filters and (∈, ∈∨q k )-fuzzyimplicative filters is established. Conditions for an (∈,∈∨q k )-fuzzy filterto be an (∈, ∈∨q k )-fuzzy implicative filter are considered. Character-izations of an (∈, ∈∨q k )-fuzzy implicative filter are provided, and theimplication-based fuzzy implicative filters of an R 0 -algebra is discussed. 1. IntroductionOne important task of artificial intelligence is to make the computers sim-ulate beings in dealing with certainty and uncertainty in information. Logicappears in a “sacred” (respectively, a “profane”) form which is dominant inproof theory (respectively, model theory). The role of logic in mathematicsand computer science is twofold – as a tool for applications in both areas, anda technique for laying the foundations. Non-classical logic including many-valued logic, fuzzy logic, etc., takes the advantage of classical logic to handleinformation with various facets of uncertainty (see [11] for generalized theory ofuncertainty), such as fuzziness, randomness etc. Non-classical logic has becomea formal and useful tool for computer science to deal with fuzzy informationand uncertain information. Among all kinds of uncertainties, incomparabil-ity is an important one which can be encountered in our life. The conceptof R